We adopt the notion of von Neumann-Morgenstern farsightedly stable sets to predict which matchings are possibly stable when agents are farsighted in one-to-one matching problems. We provide the characterization of von Neumann-Morgenstern farsightedly stable sets: a set of matchings is a von Neumann-Morgenstern farsightedly stable set if and only if it is a singleton set and its element is a corewise stable matching. Thus, contrary to the von Neumann-Morgenstern (myopically) stable sets, von Neumann-Morgenstern farsightedly stable sets cannot include matchings that are not corewise stable ones. Moreover, we show that our main result is robust to many- to-one matching problems with responsive preferences.